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 A133161 Indices of the triangular numbers which are also centered triangular number. 2
 1, 4, 16, 61, 229, 856, 3196, 11929, 44521, 166156, 620104, 2314261, 8636941, 32233504, 120297076, 448954801, 1675522129, 6253133716, 23337012736, 87094917229, 325042656181, 1213075707496, 4527260173804, 16895964987721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, indices of the triangular numbers which are sums of three consecutive triangular numbers (see A129803). LINKS A. Kozikowska, Topological classes of statically determinate beams with arbitrary number of supports, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; (see Eq. 5.18). - N. J. A. Sloane, Dec 17 2011. Index entries for linear recurrences with constant coefficients, signature (5,-5,1). FORMULA a(n+2)=4*a(n+1)-a(n)+1. a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5. G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - R. J. Mathar, Oct 24 2007 a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(3/4)*[2-sqrt(3)]^n+(3/4) *[2+sqrt(3)]^n, with n>=0 - Paolo P. Lava, Jul 30 2008 a(n)-a(n-1)= A005320(n-1). - R. J. Mathar, Mar 14 2016 MATHEMATICA LinearRecurrence[{5, -5, 1}, {1, 4, 16}, 30] (* Harvey P. Dale, Aug 29 2017 *) CROSSREFS Cf. A001834, A102871, A128862, A129803, A001571. Sequence in context: A203153 A126929 A268452 * A103820 A206570 A206790 Adjacent sequences:  A133158 A133159 A133160 * A133162 A133163 A133164 KEYWORD nonn,easy AUTHOR Richard Choulet, Oct 09 2007 STATUS approved

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Last modified August 16 00:25 EDT 2018. Contains 313782 sequences. (Running on oeis4.)